On 1-bend Upward Point-set Embeddings of $st$-digraphs

Fuente: arXiv
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Auteurs principaux: Di Giacomo, Emilio, Förster, Henry, Kokhovich, Daria, Mchedlidze, Tamara, Montecchiani, Fabrizio, Symvonis, Antonios, Villedieu, Anaïs
Format: Preprint
Publié: 2024
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author Di Giacomo, Emilio
Förster, Henry
Kokhovich, Daria
Mchedlidze, Tamara
Montecchiani, Fabrizio
Symvonis, Antonios
Villedieu, Anaïs
author_facet Di Giacomo, Emilio
Förster, Henry
Kokhovich, Daria
Mchedlidze, Tamara
Montecchiani, Fabrizio
Symvonis, Antonios
Villedieu, Anaïs
contents We study the upward point-set embeddability of digraphs on one-sided convex point sets with at most 1 bend per edge. We provide an algorithm to compute a 1-bend upward point-set embedding of outerplanar $st$-digraphs on arbitrary one-sided convex point sets. We complement this result by proving that for every $n \geq 18$ there exists a $2$-outerplanar $st$-digraph $G$ with $n$ vertices and a one-sided convex point set $S$ so that $G$ does not admit a 1-bend upward point-set embedding on $S$.
format Preprint
id arxiv_https___arxiv_org_abs_2401_03226
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On 1-bend Upward Point-set Embeddings of $st$-digraphs
Di Giacomo, Emilio
Förster, Henry
Kokhovich, Daria
Mchedlidze, Tamara
Montecchiani, Fabrizio
Symvonis, Antonios
Villedieu, Anaïs
Computational Geometry
We study the upward point-set embeddability of digraphs on one-sided convex point sets with at most 1 bend per edge. We provide an algorithm to compute a 1-bend upward point-set embedding of outerplanar $st$-digraphs on arbitrary one-sided convex point sets. We complement this result by proving that for every $n \geq 18$ there exists a $2$-outerplanar $st$-digraph $G$ with $n$ vertices and a one-sided convex point set $S$ so that $G$ does not admit a 1-bend upward point-set embedding on $S$.
title On 1-bend Upward Point-set Embeddings of $st$-digraphs
topic Computational Geometry
url https://arxiv.org/abs/2401.03226